Pseudo EMV-algebras. I. basic properties

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73597650" target="_blank" >RIV/61989592:15310/19:73597650 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.researchgate.net/publication/337464364_Pseudo_EMV-algebras_I_Basic_Properties" target="_blank" >https://www.researchgate.net/publication/337464364_Pseudo_EMV-algebras_I_Basic_Properties</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Pseudo EMV-algebras. I. basic properties

Popis výsledku v původním jazyce

We introduce pseudo EMV-algebras which are a non-commutative generalization of both MV-algebras and generalized Boolean algebras. The existence of a top element is not assumed. The paper has two parts. In the present one we study basic properties of pseudo EMV-algebras as ideals and homomorphisms. The class of all pseudo EMV-algebras is not a variety and rather a more general class, called a q-variety, but similar to a variety. We study representable pseudo EMV-algebras, normal-valued ones, and pseudo EMV-algebras whose every maximal ideal is normal. The second part shows that every pseudo EMV-algebra without top element can be embedded into a pseudo EMV-algebra with top element as a maximal and normal ideal of the latter one. We present a categorical equivalence of the category of pseudo EMV-algebras without top element with a special category of pseudo MV-algebras or with a special category of ℓ-groups. Finally, we study states as finitely additive mappings as well as state-morphisms on pseudo EMV-algebras and we present their representation as an integral over a regular Borel probability measure.

Název v anglickém jazyce

Pseudo EMV-algebras. I. basic properties

Popis výsledku anglicky

We introduce pseudo EMV-algebras which are a non-commutative generalization of both MV-algebras and generalized Boolean algebras. The existence of a top element is not assumed. The paper has two parts. In the present one we study basic properties of pseudo EMV-algebras as ideals and homomorphisms. The class of all pseudo EMV-algebras is not a variety and rather a more general class, called a q-variety, but similar to a variety. We study representable pseudo EMV-algebras, normal-valued ones, and pseudo EMV-algebras whose every maximal ideal is normal. The second part shows that every pseudo EMV-algebra without top element can be embedded into a pseudo EMV-algebra with top element as a maximal and normal ideal of the latter one. We present a categorical equivalence of the category of pseudo EMV-algebras without top element with a special category of pseudo MV-algebras or with a special category of ℓ-groups. Finally, we study states as finitely additive mappings as well as state-morphisms on pseudo EMV-algebras and we present their representation as an integral over a regular Borel probability measure.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Applied Logics-IfCoLoG Journal of Logics and their Applications

ISSN

2055-3706

e-ISSN

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Svazek periodika

6

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

43

Strana od-do

1285-1327

Kód UT WoS článku

000519571900005

EID výsledku v databázi Scopus

2-s2.0-85076982405